Senate Democrats are looking to intensify the Russia-related investigations on Capitol Hill despite a call from Republican National Committee Chairwoman Ronna McDaniel to abandon the “collusion” track for lack of evidence – with plans to grill Attorney General Jeff Sessions and even a bid to get President Trump under oath.

While Trump has not responded to the invitation, Sessions already has agreed to answer questions Tuesday before the Senate Intelligence Committee in the probe of Russian meddling in the 2016 presidential race. Presuming that hearing goes forward, the big question is whether Sessions will testify in public – and in doing so, drive the same kind of media frenzy that surrounded fired FBI Director James Comey’s testimony this past Thursday.

Senate Minority Leader Chuck Schumer, D-N.Y., said Sunday he wants Sessions speaking in public and under oath.

“There are some questions about Sessions that have to be asked,” Schumer said on CBS News’ “Face the Nation.”

Schumer, in the same interview, invited Trump to testify before the Senate, responding to the president’s Friday claim that he’d be “100 percent” willing to speak under oath. Regardless of whether Trump agrees, the pursuit of Sessions and several Trump campaign figures for questioning on Capitol Hill virtually ensures the Russia investigation will continue to play out in public and cast a continued “cloud” over the administration’s agenda – even as special counsel Robert Mueller pursues his investigation behind closed doors.

In the near-term, Schumer and fellow Democratic senators made clear they have several tough questions they want the attorney general to be asked Tuesday – preferably, before the glare of TV cameras.

On “Fox News Sunday,” Sen. Jack Reed, D-R.I., said he has questions about Sessions’ participation in Comey’s firing – considering the firing came after Sessions recused himself from the Russia probe.

“He had already recused himself and then, suddenly, he’s the one apparently recommending to the president that Comey be fired and the president has … declared it was all about the Russian investigation,” Reed said.

The Trump administration has given numerous reasons for Comey’s firing, including his handling of the Hillary Clinton email probe. But Comey testified last week that he thinks the Russia probe was the driving force.

Reed, further, said he has questions about Sessions’ past meetings with Russian officials beyond those he’s already declared.

“That will come up,” he vowed.

Schumer said Sessions should be asked whether he interfered in the Russia investigation before his recusal; what safeguards are in place now; and whether he discussed the Russia issue in the search for a new FBI director.

During his testimony last week, Comey suggested there might be more to Sessions’ recusal from the Russia probe, telling lawmakers he believed it was “inevitable” that Sessions would recuse himself and there were “facts” he could not discuss in an open hearing.

The Department of Justice, however, issued a statement standing by the original explanation that Sessions recused himself due to his participation in Trump’s campaign.

“[I]t was for that reason, and that reason alone,” spokesman Ian Prior said.

Sessions had been set to testify before a budget-related subcommittee on Tuesday but, in letters to key lawmakers, said the intelligence committee that heard from Comey would be the more appropriate venue considering the Russia-related questions.

Sen. James Lankford, R-Okla., a member of that committee, said on “Face the Nation” that they have not yet finalized whether the attorney general’s testimony will be public or private.

“I assume that this will be public, but we are still in that final conversation time with Jeff Sessions,” Lankford said.

He said it’s important to hear Sessions’ “side of the story” regarding some of Comey’s claims last week “as well as these accusations that are flying out there about conversations that he might or might not have had with Russians prior to the election.”

On “Fox News Sunday,” McDaniel appealed to lawmakers to drop their line of investigation regarding the question of collusion between the Trump campaign and Moscow.

“This is a fishing expedition,” she said. “I’m calling for an end to the investigations about … President Trump’s campaign colluding with the Russians. There’s been no evidence of it; I don’t think that should continue.”

Democrats made clear they have no such plans.

Sen. Dianne Feinstein, D-Calif., top Democrat on the Senate Judiciary Committee, said on CNN’s “State of the Union” that “it should be all hands on deck” for lawmakers examining the case.

Feinstein, who also sits on the intelligence panel, could not say whether the Sessions hearing would be public or whether it would even go forward. She also raised the possibility of yet another hearing, saying the judiciary committee would be the “fitting” venue for the attorney general’s testimony.

As for what lawmakers should be exploring, Feinstein did not mince words, saying they should examine “the technical legal aspects of obstruction of justice.”

Trump’s allies have downplayed the obstruction angle, noting Comey stopped short of alleging obstruction of justice in his testimony and said Trump did not try to push him to end the Russia probe as a whole.